The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1 X^2  1  0  1  1  1  1  1  X  1  X  X  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1 X^2+1  1  X X^2  1 X+1  1  0 X^2+X+1 X+1 X^2  1  1 X^2+X X^2  1  0
 0  0  X  0 X^2+X  0 X^2+X  0  X X^2  X  X  X X^2+X  0  0 X^2 X^2+X X^2 X^2+X X^2+X X^2+X  0  X X^2+X  0
 0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+52x^20+100x^21+222x^22+252x^23+595x^24+408x^25+837x^26+440x^27+587x^28+244x^29+205x^30+76x^31+40x^32+16x^33+15x^34+5x^36+1x^38

The gray image is a linear code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 0.239 seconds.